Lesson 5 | Proportional Relationships | 7th Grade Mathematics

Objective

Write equations for proportional relationships from word problems.

Common Core Standards

Core Standards

The core standards covered in this lesson

7.RP.A.2 — Recognize and represent proportional relationships between quantities.

Ratios and Proportional Relationships

7.RP.A.2 — Recognize and represent proportional relationships between quantities.
7.RP.A.2.C — Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

Ratios and Proportional Relationships

7.RP.A.2.C — Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

Foundational Standards

The foundational standards covered in this lesson

6.EE.B.7

Expressions and Equations

6.EE.B.7 — Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
6.EE.C.9

Expressions and Equations

6.EE.C.9 — Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Recall that a ratio relationship $$A:B$$ has two unit rates, $$A/B$$ and $$B/A$$.
Find the constant of proportionality from a situation (not a table) by finding the value of $$y/x$$, where $$y$$ is the dependent variable and $$x$$ is the independent variable.
Write an equation using the constant of proportionality for a proportional relationship.
Use an equation to solve problems.
Decontextualize situations to represent them as equations and re-contextualize equations to explain their meanings as they relate to situations (MP.2).

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Lesson Materials

Calculators (1 per student)

Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

Problem 1

A repair technician replaces cracked screens on phones. He can replace 5 screens in 3 hours.

a. Write an equation you can use to determine how long it takes to replace any number of screens.

b. Write an equation you can use to determine how many screens can be replaced in a certain number of hours.

c. Use one of your equations to determine how long it would take to replace 30 screens.

d. Use one of your equations to determine how many screens could be replaced in 12 hours.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem 2

A train traveling from Boston to New York moves at a constant speed. The train covers 260 miles in 3.25 hours.

Write an equation that represents this relationship. Explain what your equation tells you about the train.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem 3

Deli turkey meat is on sale at two different grocery stores, as represented below.

Stop & Buy

$$c=6.25p$$, where $$c$$ represents cost in dollars and $$p$$ represents number of pounds of turkey

Roger's

Amount (pounds)	Cost ($)
3	19.50
4	26.00
6	39.00
7	45.50

What is the unit price of turkey per pound at each store? Which store has the better sale?

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem Set

A set of suggested resources or problem types that teachers can turn into a problem set

Fishtank Plus Content

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

The 7th graders at Wilson Middle School are taking a field trip to the science museum. So far, 12 students have turned in a total of $81 to pay for their ticket.

a. Write an equation to represent the cost, $$c$$, for $$t$$ tickets.

b. If all 72 students turn in their ticket money, how much money will be collected?

Student Response

Create a free account or sign in to view Student Response

Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

Challenge: The average person uses about 90 gallons of water per day. At this rate, how long would it take a family of 4 to use enough water to fill an average-size swimming pool? An olympic-size swimming pool?

EngageNY Mathematics Grade 7 Mathematics > Module 1 > Topic B > Lesson 8 — Problem Set 1-4; Do not include any questions with graphs as these will be addressed in upcoming lessons.
Open Up Resources Grade 7 Unit 2 Practice Problems — Lesson 5
EngageNY Mathematics Grade 7 Mathematics > Module 1 > Topic B > Lesson 9 — Example 1, Problem Set 1 and 3
Illustrative Mathematics Sore Throats, Variation 1
RDA Performance Task Bank Grade 7 Mathematics Sample SR Item

Lesson 4

Lesson 6

Lesson Map

Topic A: Representing Proportional Relationships in Tables, Equations, and Graphs

Solve ratio and rate problems using double number lines, tables, and unit rate.

7.RP.A.1 7.RP.A.2

Represent proportional relationships in tables, and define the constant of proportionality.

7.RP.A.2 7.RP.A.2.B

Determine the constant of proportionality in tables, and use it to find missing values.

7.RP.A.2.A 7.RP.A.2.B

Write equations for proportional relationships presented in tables.

7.RP.A.2.B 7.RP.A.2.C

Write equations for proportional relationships from word problems.

7.RP.A.2 7.RP.A.2.C

Represent proportional relationships in graphs.

7.RP.A.2 7.RP.A.2.A 7.RP.A.2.D

Interpret proportional relationships represented in graphs.

7.RP.A.2 7.RP.A.2.D

Topic B: Non-Proportional Relationships

Compare proportional and non-proportional relationships.

7.RP.A.2.A

Determine if relationships are proportional or non-proportional.

7.RP.A.2.A

Topic C: Connecting Everything Together

Make connections between the four representations of proportional relationships (Part 1).

7.RP.A.2 7.RP.A.2.A 7.RP.A.2.B 7.RP.A.2.C 7.RP.A.2.D

Make connections between the four representations of proportional relationships (Part 2).

7.RP.A.2 7.RP.A.2.A 7.RP.A.2.B 7.RP.A.2.C 7.RP.A.2.D

Use different strategies to represent and recognize proportional relationships.

7.RP.A.2 7.RP.A.2.A 7.RP.A.2.B 7.RP.A.2.C 7.RP.A.2.D

Topic D: Solving Ratio & Rate Problems with Fractions

Find the unit rate of ratios involving fractions.

7.RP.A.1

Find the unit rate and use it to solve problems.

7.RP.A.1 7.RP.A.3

Solve ratio and rate problems by setting up a proportion.

7.RP.A.1 7.RP.A.3

Solve ratio and rate problems by setting up a proportion, including part-part-whole problems.

7.RP.A.1 7.RP.A.3

Solve multi-step ratio and rate problems using proportional reasoning, including fractional price increase and decrease, commissions, and fees.

7.RP.A.3

Use proportional reasoning to solve real-world, multi-step problems.

7.RP.A.1 7.RP.A.2 7.RP.A.3

Proportional Relationships

Objective

Common Core Standards

Core Standards

Ratios and Proportional Relationships

Ratios and Proportional Relationships

Foundational Standards

Expressions and Equations

Expressions and Equations

Criteria for Success

Tips for Teachers

Lesson Materials

Anchor Problems

Problem 1

Guiding Questions

Problem 2

Guiding Questions

Problem 3

Guiding Questions

Problem Set

Target Task

Student Response

Additional Practice

Lesson Map

Request a Demo

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Any other information you would like to provide about your school?

Effective Instruction Made Easy